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Theorem i5lei4 350
 Description: Relevance implication is less than or equal to non-tollens implication. (Contributed by NM, 26-Jun-2003.)
Assertion
Ref Expression
i5lei4 (a5 b) ≤ (a4 b)

Proof of Theorem i5lei4
StepHypRef Expression
1 leo 158 . . . 4 a ≤ (ab)
21leran 153 . . 3 (ab ) ≤ ((ab) ∩ b )
32lelor 166 . 2 (((ab) ∪ (ab)) ∪ (ab )) ≤ (((ab) ∪ (ab)) ∪ ((ab) ∩ b ))
4 df-i5 48 . 2 (a5 b) = (((ab) ∪ (ab)) ∪ (ab ))
5 df-i4 47 . 2 (a4 b) = (((ab) ∪ (ab)) ∪ ((ab) ∩ b ))
63, 4, 5le3tr1 140 1 (a5 b) ≤ (a4 b)
 Colors of variables: term Syntax hints:   ≤ wle 2  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →4 wi4 15   →5 wi5 16 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38 This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i4 47  df-i5 48  df-le1 130  df-le2 131 This theorem is referenced by: (None)
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